Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C17×#555 ⋊ C2 |
| Sylow | C17 ⋊ #1624 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #10587639 |
| commutator, cosocle | C42×C17 | C23 |
| Frattini | C42 | C22×D17 |
| Fitting | C17×#555 | C2 |
| socle | C22×C17 | #120 |
| hypercenter | #555 | D17 |
| hypocenter | C17 | #1624 |
| LCS | G ▷ C42×C17 ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #555 | |
240 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|b^2=f,c^2=fg,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^16,d^b=df,e^b=eg,d^c=dg,e^c=eg226 conjugacy classes — view the full character table.
| maximal subgroup of | #16955081, D17×#1624, C2×#14527867, … |
| maximal normal subgroup of | #16955081, D17×#1624, C2×#14527867, … |
| maximal quotient of | #16923069, #16923074, #16923088, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 3593);